CN100385214C - Nonlinear spectrum similarity measurement method - Google Patents

Abstract

The present invention relates to a nonlinear spectrum similarity measurement method which belongs to the technical field of information. Firstly, in the present invention, a kernel principal component analysis method is adopted to remove the strong correlation between spectral wavebands. More specifically, the present invention aims at the strong correlation between the spectrum wavebands and uses nonlinear transformation to transform original spectrum vectors into a new characteristic space. In the characteristic space, a kernel function and the principal component analysis method are used for obtaining characteristic values and characteristic vectors of all nonzero characteristics in a covariance matrix. The characteristic values are ranged in descending order, and the characteristic vectors corresponding to the first N characteristic values are selected. Thus, a standard orthogonal basis is structured, and the spectral vectors in the characteristic space are finally projected onto the standard orthogonal basis. Secondly, spectral reflection and absorptive characteristics are merged. More specifically, a reflectivity vector and a normalized absorbance vector are correspondingly multiplied with a waveband value, and thus, a compound spectral vector is formed. The present invention can be used for removing the strong correlation between the wavebands, and is compatible with the functions of the spectral reflection and the absorptive characteristics in the spectral similarity measurement at the same time.

Description

The non-linear spectral method for measuring similarity

Technical field

The present invention relates to a kind of spectral measurements method, specifically is a kind of based on the reflection of the complete waveform of spectrum and the non-linear spectral method for measuring similarity of absorption feature.Belong to areas of information technology.

Background technology

Find that by literature search the spectral similarity measure can be divided into two classes, a class is based on complete waveform character, typical method such as the drawing of spectrum angle.Kruse, " the visual and analysis of spectrum picture disposal system-optical spectrum imagers data interaction " (1993b that people such as FA deliver in U.S.'s " environmental remote sensing ", The SpectralImage Processing System (SIPS)-Interactive Visualization and Analysisof Imaging Spectrometer Data.Remote Sensing nvironment, 44:145-163), this article has proposed spectrum angle drafting method, promptly utilizes angle between the spectral reflectivity vector to go to measure similarity between spectrum.The advantage of this method is that it can overcome the influence of intensity of illumination to spectral similarity tolerance.Yet this method has only been considered the effect of spectral reflectivity in similarity measurement on the one hand, does not consider the strong correlation between spectral band on the other hand.Another kind of spectroscopic diagnostics absorption feature, the method for curve such as the spectral absorption index of being based on.People such as Wang Jinnian are at " environmental remote sensing " Vol.11, " imaging spectral image spectral absorption discriminating model and mineral map plotting research " literary composition of delivering on the No.1.Feb 1996, and this article has proposed spectral absorption evaluation model, i.e. the spectral absorption index certificate of a correction.This method is suitable for that spectrum specific absorption peak is carried out similarity and passes judgment on, this method itself also is not suitable for similarity measurement between any spectrum, yet this method has reflected that the contribution that the spectrum different-waveband is measured spectral similarity is different, and its shortcoming is the complete waveform of having ignored the reflectance signature of spectrum and can not being applicable to spectrum.The reflection of spectrum and to absorb feature be indivisible two category features of spectrum, however present spectral similarity measure is only at a kind of feature wherein.In addition, present spectral similarity degree method is all supposed between spectral band independently of one another, however this hypothesis do not tally with the actual situation, the strong correlation between spectral band at present is widely applied in the dimensionality reduction and feature extraction of spectroscopic data.

Summary of the invention

The objective of the invention is to above-mentioned deficiency at prior art, a kind of non-linear spectral method for measuring similarity is proposed, promptly based on the reflection of complete waveform and the non-linear spectral method for measuring similarity of absorption feature, make it can remove strong correlation between wave band on the one hand, taken into account spectral reflectance on the other hand and absorbed the effect of feature in spectral similarity tolerance.

The present invention is achieved by the following technical solutions, and the inventive method comprises two key links, and one is that employing core principle component analysis method has been removed the strong correlation between the spectral band, and another is spectral reflectance and the merging that absorbs feature.

1 adopts the strong correlation between the core principle component analysis method removal spectral band

At the strong correlation between spectral band, at first utilize nonlinear transformation with original spectrum vector transformation to a new feature space.Then, in feature space, utilize kernel function and principal component analytical method to obtain covariance matrix all non-zero characteristics eigenwert and proper vectors, eigenwert is pressed descending sort, select top n (N is the spectral band number) eigenwert characteristic of correspondence vector, and construct one group of orthonormal basis with this.At last, with spectrum vector projection in the feature space to orthonormal basis.

The merging of 2 spectral reflectances and absorption feature

The continuum curve is meant the outer wrapping curve of the curve of spectrum, and when actual treatment, the continuum curve is that the straight line with segmentation comes approximate representation.Continuum is removed the ratio that curve is meant the curve of spectrum and continuum curve, and it has kept the spectral absorption peak, and reflection peak is normalized to 1, is shown below:

${\stackrel{\→}{r}}_{\mathrm{cr}}=\stackrel{\→}{r}/{\stackrel{\→}{r}}_c---\left(1\right)$

Wherein,

Be that continuum is removed curve, Be spectrum,

Be and spectrum The corresponding continuum curve of wave band.The absorption feature of spectrum (as the symmetry of the degree of depth, width, wave band position and the absorption peak that absorb etc.) can be removed curve according to continuum and obtain, but with the absorption feature of spectrum as factor of similarity measurement, see expression formula (2).

$\stackrel{\→}{R}=\stackrel{\→}{r}\×{\stackrel{\→}{r}}_{\mathrm{cr}}---\left(2\right)$

Wherein,

In addition continuum is removed the non-linear spectral vector of curve constraint,

Be to project to the later spectrum vector of orthonormal basis in the feature space,

The continuum that is spectrum is removed curve.

Below the present invention is further illustrated, the method concrete steps are as follows:

(1) select kernel function and parameter is set, the kernel function of choosing is the polar coordinates kernel functions

$(k(x,y)=\exp (-\frac{{\left|\right|x-y\left|\right|}^2}{\mathrm{\δ}})),(\mathrm{\δ}=2);$

(2) utilize kernel function to obtain nuclear matrix K,, in original spectrum vector projection to a Hilbert inner product space, be actually the nonlinear transformation of having finished an implicit expression by kernel function;

(3) by calculating eigenwert and the proper vector that obtains nuclear matrix K;

(4) eigenwert and the proper vector of N non-zero of selection, and proper vector is carried out zero-mean handle, wherein N is the spectral band number, why selects eigenwert and the proper vector the same with the spectral band number, is to merge (suc as formula 2) for the absorption feature with the back;

(5) with spectrum vector projections all in the feature space to the normal coordinates base of selecting that proper vector constituted;

(6) reflectance signature behind the combined transformation and absorption feature are seen formula 2.

(7) utilize the drawing of spectrum angle that the later vector of conversion is carried out similarity measurement.

The present invention mainly contains the innovative point of two aspects, utilize on the one hand core principle component analysis to remove strong correlation between spectral band, thereby it is consistent that the spectrum vector and the prerequisite of spectrum angle drawing tolerance are supposed, is separate between each wave band promptly.Take all factors into consideration the reflection of spectrum on the other hand and absorbed the effect of feature in similarity measurement, strengthened the effect of spectral absorption peak in similarity measurement.This method had both overcome spectrum angle drafting method and had not considered strong correlation between spectral band, overcome drawing of spectrum angle and spectral absorption index again and only considered the shortcoming of a certain feature (absorbing feature or reflectance signature) of spectrum, in addition, this method has made full use of the advantage of drawing of spectrum angle and spectral absorption index, i.e. it is that to contribute be different to different-waveband in the advantage of spectral similarity tolerance influence and the spectral absorption index to the weight of spectral similarity tolerance that spectrum angle drawing can overcome intensity of illumination.

Embodiment

For understanding technical scheme of the present invention better, the realization to this method is further described in conjunction with the embodiments.

At first, select kernel function and necessary parameter is set.In the case study on implementation below, the kernel function of choosing is $(k(x,y)=\exp \left(\frac{{\left|\right|x-y\left|\right|}^2}{\mathrm{\δ}}\right)),$ (δ＝2)。Then, utilize kernel function calculate by covariance matrix and and nuclear matrix that proper vector derived, and calculate the eigenwert and the proper vector of this matrix.Secondly, construct one group of orthonormal basis according to these proper vectors, and the projection of spectrum vector on orthogonal basis in the calculated characteristics space.Once more, merge in the spectrum vector according to the absorption feature of formula (2) spectrum.At last, with metric function the later spectrum vector of conversion is carried out similarity measurement.

Content in conjunction with the inventive method provides following examples:

Library of spectra (spc_lib04a) with US Geological Survey (USGS) is a data source, and the spectrum in this library of spectra is carried out the similarity retrieval experiment.Total totally 498 spectrum in the library of spectra, the wave band number of spectrum is 444, and wavelength is between 0.2 to 3.0 micron, and spectral resolution is less than waiting 10 nanometers (Clark, 1993).The particulars of relevant this library of spectra can be with reference to network address Http:// speclab.cr.usgs.gov/spectral.lib04/clark1993/spectral lib.html

With haematite (Hematite_FE2606) is reference spectra, and the similarity measurement function is spectrum angle drawing (being the angle between the vector), carries out the similarity retrieval experiment, and experimental result is as follows: the waveform of 16 spectrum that (1) is the most similar; (2) the most similar 16 spectrum titles, mineral type and mineral compositions (seeing Table 1); (3) belong to the ordering (see Table 2) of 12 spectrum in similarity retrieval of haematite in the library of spectra.

From three aspects result for retrieval is estimated: (1) retrieval precision, it is meant that spectrum similar with parameter spectrum in the result for retrieval that returns accounts for the ratio of overall result; (2) recall rate, it is in the spectrum similar with reference spectra, the shared proportion of similar spectrum that returns; (3) similar spectrum sorts at spectral similarity.

16 spectrum titles that table 1 is the most similar and mineral type

Ordering and the spectrum angle of the spectrum of all haematite classes of table 2 in similarity retrieval

As can be seen from Table 1: from the mineral classification, in non-linear spectral drawing retrieval, the spectrum that belongs to haematite has 10, and in the drafting method of spectrum angle, has only 7 to belong to the haematite class (1); (2) from mineral type, in nonlinear optical spectral corner drawing retrieval, the spectrum that belongs to oxide has 12, and in the drafting method of spectrum angle, the spectrum that belongs to oxide has only 9; (3) formation of spectral absorption characteristics mainly be since in the mineral electronic transition and molecular vibration (Clark, R.N.199), therefore, the composition of mineral is to a certain degree determining the diagnostic waveform of spectrum.From mineral composition, contain the spectrum of Alpha-Fe203, have 14 in the non-linear spectral drafting method under the continuum constraint, and have only 10 in the drafting method of spectrum angle; Therefore, analyze from 16 spectrum of the similarity of two kinds of methods, nonlinear optical spectral corner drafting method will obviously be better than spectrum angle drafting method.From above three angles that different spectrum is similar, the result of calculation of retrieval precision sees Table 3.

The table 3 liang class methods retrieval precision table of comparisons

Method for measuring similarity	Spectrum types	Mineral type	Mineral composition
				The drawing of spectrum angle	0.437	0.563	0.625
The drawing of nonlinear optical spectral corner	0.625	0.75	0.875

In addition, from the mineral classification, the recall rate of the retrieval at spectrum angle is 0.583, and the recall rate of non-linear spectral angle drafting method is 0.833.

As can be seen from Table 2: belong in 12 spectrum ordering that all spectral similarities are measured in library of spectra of haematite, for nonlinear optical spectral corner drafting method, 10 spectrum are in being in 16 the most similar result for retrieval, and maximum sequence number is 25.Yet in the drafting method of spectrum angle, have only 7 to be in 16 the most similar result for retrieval, in addition, its maximum sequence number has reached 96, and greater than have 5 of sequence number 25.

Therefore, from the angle of spectrum class similarity retrieval, nonlinear optical spectral corner drafting method obviously is better than spectrum angle drafting method.

Claims (1)

1. non-linear spectral method for measuring similarity is characterized in that concrete steps are as follows:

(1) selects kernel function and correlation parameter is set;

(2) utilize kernel function to obtain nuclear matrix K,, in original spectrum vector projection to a Hilbert inner product space, finish the nonlinear transformation of an implicit expression by kernel function;

(3) by calculating eigenwert and the proper vector that obtains nuclear matrix K;

(4) select the eigenwert and the proper vector of N non-zero, and proper vector is carried out zero-mean handle, wherein N is the spectral band number;

(5) with spectrum vector projections all in the feature space to the normal coordinates base of selecting that proper vector constituted;

(6) reflectance signature after merging absorption feature and the conversion, the corresponding wave band value of absorptivity vector that reflectivity vector sum normalization after the nuclear conversion is later multiplies each other, thereby constitutes a compound spectrum vector;

(7) utilize spectrum angle drawing that the compound spectrum vector of new formation is carried out similarity measurement.